We formulate a statistical analogy of regular Lagrange mechanics and Finsler
geometry derived from Grisha Perelman's functionals generalized for
nonholonomic Ricci flows. There are elaborated explicit constructions when
nonholonomically constrained flows of Riemann metrics result in Finsler like
configurations, and inversely, and geometric mechanics is modelled on Riemann
spaces with preferred nonholonomic frame structure.